#### Glasnik Matematicki, Vol. 39, No.1 (2004), 101-110.

### STATISTICAL (*T*) RATES OF CONVERGENCE

### H. I. Miller and C. Orhan

Department of Mathematics, The University of Louisville,
Louisville, Kentucky, USA

University of Sarajevo, Department of Mathematics,
Sarajevo, 33000, Bosnia and Herzegovina

*e-mail:* `nmiller@utic.net.ba`

Department of Mathematics, Faculty of Science, Ankara
University, Tandogan 06100, Ankara, Turkey

*e-mail:* `orhan@science.ankara.edu.tr`

**Abstract.** The basis for comparing rates of convergence of
two null sequences is that
"*x* = (*x*_{n}) converges
(*stat T*) faster than
*z* = (*z*_{n}) provided that
(*x*_{n}/*z*_{n}) is
*T*-statistically convergent to zero" where
*T* = (*t*_{mn}) is a mean.
In this paper we extend the previously
known results either on the ordinary convergence or statistical
rates of convergence of two null sequences. We also consider
lacunary statistical rates of convergence.

**2000 Mathematics Subject Classification.**
40A05, 40C05.

**Key words and phrases.** Natural density, statistically
convergent sequence, rate of convergence.

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